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Theory of Optomechanical Locking in Driven-Dissipative Coupled Polariton Condensates

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posted on 2023-12-16, 17:00 authored by I. A. Ramos Pérez, I. Carraro Haddad, F. Fainstein, D. L. Chafatinos, G. Usaj, G. B. Mindlin, A. Fainstein, A. A. Reynoso
Synchronization between distant polariton condensates has been theoretically proposed and experimentally observed. It is a quite general behaviour intimate to dynamical dissipative non-linear systems, and pervasive to very different domains of nature. We theoretically study these phenomena for two coupled condensates in the presence of a fixed mechanical harmonic driving representing an electrically generated modulation, through coherent bulk acoustic waves, or self-induced optomechanical vibrations. We consider either a linear or a quadratic phonon-displacement induced modulation of the coupling between the condensates. Peculiar asynchronously locked phases are found, and are analyzed in the context of synchronization and Josephson-like oscillations phenomena that appear in the non-driven case. Some analytical analysis of the asynchronous locking is performed in the rotating wave approximation, while the more general situation is studied numerically. Arnold tongues corresponding to the asynchronously locked phases develop at condensate detunings that correspond to integer numbers of the mechanical frequency and also to rational fractions of it. Unlocked 'quasiperiodic' and chaotic regimes can also be reached. In particular, the phonon-induced fractional locking frequencies arrange in a Farey sequence that produces a Devil's staircase of the steady-state dressed detuning between the condensates. Importantly, both polariton-polariton and reservoir-polariton interactions facilitate the realization of phonon-induced asynchronously locked phases. The relation to recent experiments on optomechanically driven condensates in arrays of polariton traps is discussed.



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